CUBES AND DICE | CSAT | REASONING | UPSC CSE

Описание: CUBES AND DICE | CSAT | REASONING | UPSC CSE

Stop trying to mentally fold shapes in the exam hall! 🎲 In this mindmap video for UPSC CSE by Dr. Sonu Patel, we master **Cubes and Dice**—a highly visual and scoring topic in the CSAT Reasoning section.

UPSC loves to give you 3 or 4 different views of the same dice and ask you what lies on the opposite face. If you try to visualize the rotations, you will lose precious time. We break down the foolproof "Clockwise Rule" for closed dice, the "Alternate" trick for open unfolded dice, and the formula for painted cube problems!



🎲 *Video Mindmap: Cubes & Dice*

► *1. Standard vs. Ordinary (General) Dice*
• *Standard Dice:* The sum of any two opposite faces is ALWAYS 7. (1 is opposite 6, 2 is opposite 5, 3 is opposite 4). Therefore, the sum of any two adjacent (visible) faces can NEVER be 7.
• *Ordinary Dice:* The sum of any two adjacent faces can be 7. There are no fixed rules for opposite faces; you have to find them using the tricks below!

► *2. The "One Common Number" Trick (High Yield)*
• When two positions of the same dice are given, and exactly ONE number is common on both.
• *The Rule:* Start from the common number and write down the numbers in a *Clockwise* direction for both dice.
• Result: The numbers that line up vertically are opposite to each other! The missing number in the sequence is opposite the common number.

► *3. The "Two Common Numbers" Trick*
• When two positions of the dice are given, and TWO numbers are common on both.
• *The Rule:* Simply cancel out the two common numbers. The remaining two unpaired numbers are 100% opposite to each other!



► *4. Open / Unfolded Dice (UPSC's Favorite)*
• *The Z-Trick / Alternate Box Rule:* When a dice is unfolded into a 2D shape, start from any outer box and move in a straight line. The *alternate* boxes (skipping one in the middle) are ALWAYS opposite each other.
• Note: Two opposite faces can NEVER be seen together, and they can NEVER be hidden together. Use this to instantly eliminate wrong options!

► *5. Cutting a Painted Cube (The Formulas)*
• If a large painted cube is cut into $n$ smaller pieces along each edge:
• *3 faces painted:* Always *8* (the corners).
• *2 faces painted:* $12(n - 2)$ (the edges).
• *1 face painted:* $6(n - 2)^2$ (the centers of the faces).
• *0 faces painted (Colorless):* $(n - 2)^3$ (the hidden core).

Stop rotating shapes in your head and start applying the rules!

🔔 *Subscribe* for the next CSAT video where we begin Quantitative Aptitude!


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